Almost every set of $N\ge d+1$ orthogonal states on $d^{\otimes n}$ is locally indistinguishable

TL;DR

This paper shows that for most randomly chosen sets of orthogonal states in a multipartite quantum system, it is almost impossible to perfectly distinguish these states using only local operations and classical communication.

Contribution

It demonstrates that almost all sets of sufficiently large orthogonal states are locally indistinguishable, highlighting a fundamental limitation in quantum state discrimination.

Findings

Most random sets of orthogonal states are locally indistinguishable

Probability of perfect local distinguishability vanishes for large sets

Results apply to systems with high-dimensional subsystems

Abstract

I consider the problem of deterministically distinguishing the state of a multipartite system, from a set of $N\ge d+1$ orthogonal states, where $d$ is the dimension of each party's subsystem. It is shown that if the set of orthogonal states is chosen at random, then there is a vanishing probability that this set will be perfectly distinguishable under the restriction that the parties use only local operations on their subsystems and classical communication amongst themselves.